%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET076+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:25:07 AM UTC 2025
% Result : Theorem 0.45s 0.61s
% Output : Proof 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET076+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 04:13:08 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.45/0.61 % SZS status Theorem
% 0.45/0.61 % SZS output start Proof
% 0.45/0.61 tff(member_type, type, (
% 0.45/0.61 member: ( $i * $i ) > $o)).
% 0.45/0.61 tff(tptp_fun_Z_7_type, type, (
% 0.45/0.61 tptp_fun_Z_7: $i)).
% 0.45/0.61 tff(tptp_fun_U_0_type, type, (
% 0.45/0.61 tptp_fun_U_0: ( $i * $i ) > $i)).
% 0.45/0.61 tff(unordered_pair_type, type, (
% 0.45/0.61 unordered_pair: ( $i * $i ) > $i)).
% 0.45/0.61 tff(tptp_fun_Y_8_type, type, (
% 0.45/0.61 tptp_fun_Y_8: $i)).
% 0.45/0.61 tff(tptp_fun_X_9_type, type, (
% 0.45/0.61 tptp_fun_X_9: $i)).
% 0.45/0.61 tff(subclass_type, type, (
% 0.45/0.61 subclass: ( $i * $i ) > $o)).
% 0.45/0.61 tff(universal_class_type, type, (
% 0.45/0.61 universal_class: $i)).
% 0.45/0.61 tff(1,assumption,(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = Y!8), introduced(assumption)).
% 0.45/0.61 tff(2,plain,
% 0.45/0.61 (Y!8 = tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8))),
% 0.45/0.61 inference(symmetry,[status(thm)],[1])).
% 0.45/0.61 tff(3,plain,
% 0.45/0.61 (member(Y!8, Z!7) <=> member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), Z!7)),
% 0.45/0.61 inference(monotonicity,[status(thm)],[2])).
% 0.45/0.61 tff(4,plain,
% 0.45/0.61 (member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), Z!7) <=> member(Y!8, Z!7)),
% 0.45/0.61 inference(symmetry,[status(thm)],[3])).
% 0.45/0.61 tff(5,plain,
% 0.45/0.61 ((~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), Z!7)) <=> (~member(Y!8, Z!7))),
% 0.45/0.61 inference(monotonicity,[status(thm)],[4])).
% 0.45/0.61 tff(6,plain,
% 0.45/0.61 (^[X: $i, Y: $i] : refl((~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))) <=> (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))))),
% 0.45/0.61 inference(bind,[status(th)],[])).
% 0.45/0.61 tff(7,plain,
% 0.45/0.61 (![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))) <=> ![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.45/0.61 inference(quant_intro,[status(thm)],[6])).
% 0.45/0.61 tff(8,plain,
% 0.45/0.61 (^[X: $i, Y: $i] : rewrite((~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))) <=> (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))))),
% 0.45/0.61 inference(bind,[status(th)],[])).
% 0.45/0.61 tff(9,plain,
% 0.45/0.61 (![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))) <=> ![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.45/0.61 inference(quant_intro,[status(thm)],[8])).
% 0.45/0.61 tff(10,plain,
% 0.45/0.61 (![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))) <=> ![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.45/0.61 inference(transitivity,[status(thm)],[9, 7])).
% 0.45/0.61 tff(11,plain,
% 0.45/0.61 (^[X: $i, Y: $i] : trans(monotonicity(rewrite(((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) <=> ((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))), rewrite((subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))) <=> (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))), ((((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))) <=> (((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))))), rewrite((((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))) <=> (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))), ((((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))) <=> (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))))),
% 0.45/0.61 inference(bind,[status(th)],[])).
% 0.45/0.61 tff(12,plain,
% 0.45/0.61 (![X: $i, Y: $i] : (((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y))))) <=> ![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.45/0.61 inference(quant_intro,[status(thm)],[11])).
% 0.45/0.61 tff(13,plain,
% 0.45/0.61 (![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y))) <=> ![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y)))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(14,plain,
% 0.45/0.61 (^[X: $i, Y: $i] : rewrite((subclass(X, Y) <=> ![U: $i] : (member(U, X) => member(U, Y))) <=> (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y))))),
% 0.45/0.61 inference(bind,[status(th)],[])).
% 0.45/0.61 tff(15,plain,
% 0.45/0.61 (![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : (member(U, X) => member(U, Y))) <=> ![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y)))),
% 0.45/0.61 inference(quant_intro,[status(thm)],[14])).
% 0.45/0.61 tff(16,axiom,(![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : (member(U, X) => member(U, Y)))), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax','subclass_defn')).
% 0.45/0.61 tff(17,plain,
% 0.45/0.61 (![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y)))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.45/0.61 tff(18,plain,
% 0.45/0.61 (![X: $i, Y: $i] : (subclass(X, Y) <=> ![U: $i] : ((~member(U, X)) | member(U, Y)))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.45/0.61 tff(19,plain,(
% 0.45/0.61 ![X: $i, Y: $i] : (((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y))) & (subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))),
% 0.45/0.61 inference(skolemize,[status(sab)],[18])).
% 0.45/0.61 tff(20,plain,
% 0.45/0.61 (![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.45/0.61 tff(21,plain,
% 0.45/0.61 (![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.45/0.61 tff(22,plain,
% 0.45/0.61 ((~![X: $i, Y: $i] : (~((~((~subclass(X, Y)) | ![U: $i] : ((~member(U, X)) | member(U, Y)))) | (~(subclass(X, Y) | (~((~member(tptp_fun_U_0(Y, X), X)) | member(tptp_fun_U_0(Y, X), Y)))))))) | (~((~((~subclass(unordered_pair(X!9, Y!8), Z!7)) | ![U: $i] : ((~member(U, unordered_pair(X!9, Y!8))) | member(U, Z!7)))) | (~(subclass(unordered_pair(X!9, Y!8), Z!7) | (~((~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), unordered_pair(X!9, Y!8))) | member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), Z!7)))))))),
% 0.45/0.61 inference(quant_inst,[status(thm)],[])).
% 0.45/0.61 tff(23,plain,
% 0.45/0.61 (~((~((~subclass(unordered_pair(X!9, Y!8), Z!7)) | ![U: $i] : ((~member(U, unordered_pair(X!9, Y!8))) | member(U, Z!7)))) | (~(subclass(unordered_pair(X!9, Y!8), Z!7) | (~((~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), unordered_pair(X!9, Y!8))) | member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), Z!7))))))),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.45/0.61 tff(24,plain,
% 0.45/0.61 (((~((~subclass(unordered_pair(X!9, Y!8), Z!7)) | ![U: $i] : ((~member(U, unordered_pair(X!9, Y!8))) | member(U, Z!7)))) | (~(subclass(unordered_pair(X!9, Y!8), Z!7) | (~((~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), unordered_pair(X!9, Y!8))) | member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), Z!7)))))) | (subclass(unordered_pair(X!9, Y!8), Z!7) | (~((~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), unordered_pair(X!9, Y!8))) | member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), Z!7))))),
% 0.45/0.61 inference(tautology,[status(thm)],[])).
% 0.45/0.61 tff(25,plain,
% 0.45/0.61 (subclass(unordered_pair(X!9, Y!8), Z!7) | (~((~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), unordered_pair(X!9, Y!8))) | member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), Z!7)))),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.45/0.61 tff(26,plain,
% 0.45/0.61 ((~![X: $i, Y: $i, Z: $i] : ((~(member(X, Z) & member(Y, Z))) | subclass(unordered_pair(X, Y), Z))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(member(X, Z) & member(Y, Z))) | subclass(unordered_pair(X, Y), Z)))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(27,plain,
% 0.45/0.61 ((~![X: $i, Y: $i, Z: $i] : ((member(X, Z) & member(Y, Z)) => subclass(unordered_pair(X, Y), Z))) <=> (~![X: $i, Y: $i, Z: $i] : ((~(member(X, Z) & member(Y, Z))) | subclass(unordered_pair(X, Y), Z)))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(28,axiom,(~![X: $i, Y: $i, Z: $i] : ((member(X, Z) & member(Y, Z)) => subclass(unordered_pair(X, Y), Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','unordered_pair_is_subset')).
% 0.45/0.61 tff(29,plain,
% 0.45/0.61 (~![X: $i, Y: $i, Z: $i] : ((~(member(X, Z) & member(Y, Z))) | subclass(unordered_pair(X, Y), Z))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.45/0.61 tff(30,plain,
% 0.45/0.61 (~![X: $i, Y: $i, Z: $i] : ((~(member(X, Z) & member(Y, Z))) | subclass(unordered_pair(X, Y), Z))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.45/0.61 tff(31,plain,
% 0.45/0.61 (~![X: $i, Y: $i, Z: $i] : ((~(member(X, Z) & member(Y, Z))) | subclass(unordered_pair(X, Y), Z))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.45/0.61 tff(32,plain,
% 0.45/0.61 (~![X: $i, Y: $i, Z: $i] : ((~(member(X, Z) & member(Y, Z))) | subclass(unordered_pair(X, Y), Z))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.45/0.61 tff(33,plain,(
% 0.45/0.61 ~((~(member(X!9, Z!7) & member(Y!8, Z!7))) | subclass(unordered_pair(X!9, Y!8), Z!7))),
% 0.45/0.61 inference(skolemize,[status(sab)],[32])).
% 0.45/0.61 tff(34,plain,
% 0.45/0.61 (~subclass(unordered_pair(X!9, Y!8), Z!7)),
% 0.45/0.61 inference(or_elim,[status(thm)],[33])).
% 0.45/0.61 tff(35,plain,
% 0.45/0.61 ((~(subclass(unordered_pair(X!9, Y!8), Z!7) | (~((~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), unordered_pair(X!9, Y!8))) | member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), Z!7))))) | subclass(unordered_pair(X!9, Y!8), Z!7) | (~((~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), unordered_pair(X!9, Y!8))) | member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), Z!7)))),
% 0.45/0.61 inference(tautology,[status(thm)],[])).
% 0.45/0.61 tff(36,plain,
% 0.45/0.61 ((~(subclass(unordered_pair(X!9, Y!8), Z!7) | (~((~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), unordered_pair(X!9, Y!8))) | member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), Z!7))))) | (~((~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), unordered_pair(X!9, Y!8))) | member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), Z!7)))),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.45/0.61 tff(37,plain,
% 0.45/0.61 (~((~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), unordered_pair(X!9, Y!8))) | member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), Z!7))),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[36, 25])).
% 0.45/0.61 tff(38,plain,
% 0.45/0.61 (((~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), unordered_pair(X!9, Y!8))) | member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), Z!7)) | (~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), Z!7))),
% 0.45/0.61 inference(tautology,[status(thm)],[])).
% 0.45/0.61 tff(39,plain,
% 0.45/0.61 (~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), Z!7)),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.45/0.61 tff(40,plain,
% 0.45/0.61 (~member(Y!8, Z!7)),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[39, 5])).
% 0.45/0.61 tff(41,plain,
% 0.45/0.61 (member(X!9, Z!7) & member(Y!8, Z!7)),
% 0.45/0.61 inference(or_elim,[status(thm)],[33])).
% 0.45/0.61 tff(42,plain,
% 0.45/0.61 (member(Y!8, Z!7)),
% 0.45/0.61 inference(and_elim,[status(thm)],[41])).
% 0.45/0.61 tff(43,plain,
% 0.45/0.61 ($false),
% 0.45/0.61 inference(unit_resolution,[status(thm)],[42, 40])).
% 0.45/0.61 tff(44,plain,(~(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = Y!8)), inference(lemma,lemma(discharge,[]))).
% 0.45/0.61 tff(45,plain,
% 0.45/0.61 (^[U: $i, X: $i, Y: $i] : refl((~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y)))) <=> (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y)))))),
% 0.45/0.61 inference(bind,[status(th)],[])).
% 0.45/0.61 tff(46,plain,
% 0.45/0.61 (![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y)))) <=> ![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))),
% 0.45/0.61 inference(quant_intro,[status(thm)],[45])).
% 0.45/0.61 tff(47,plain,
% 0.45/0.61 (^[U: $i, X: $i, Y: $i] : trans(trans(monotonicity(rewrite((member(U, universal_class) & ((U = Y) | (U = X))) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X)))))), ((member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))) <=> (member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X)))))))), rewrite((member(U, unordered_pair(X, Y)) <=> (~((~member(U, universal_class)) | (~((U = Y) | (U = X)))))) <=> (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))), ((member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))) <=> (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y)))))), rewrite((~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y)))) <=> (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))), ((member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))) <=> (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))))),
% 0.45/0.61 inference(bind,[status(th)],[])).
% 0.45/0.61 tff(48,plain,
% 0.45/0.61 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))) <=> ![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))),
% 0.45/0.61 inference(quant_intro,[status(thm)],[47])).
% 0.45/0.61 tff(49,plain,
% 0.45/0.61 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))) <=> ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.45/0.61 inference(rewrite,[status(thm)],[])).
% 0.45/0.61 tff(50,plain,
% 0.45/0.61 (^[U: $i, X: $i, Y: $i] : rewrite((member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = X) | (U = Y)))) <=> (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X)))))),
% 0.45/0.61 inference(bind,[status(th)],[])).
% 0.45/0.61 tff(51,plain,
% 0.45/0.61 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = X) | (U = Y)))) <=> ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.45/0.61 inference(quant_intro,[status(thm)],[50])).
% 0.45/0.61 tff(52,axiom,(![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = X) | (U = Y))))), file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax','unordered_pair_defn')).
% 0.45/0.61 tff(53,plain,
% 0.45/0.61 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.45/0.61 tff(54,plain,
% 0.45/0.61 (![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.45/0.61 tff(55,plain,(
% 0.45/0.61 ![U: $i, X: $i, Y: $i] : (member(U, unordered_pair(X, Y)) <=> (member(U, universal_class) & ((U = Y) | (U = X))))),
% 0.45/0.61 inference(skolemize,[status(sab)],[54])).
% 0.45/0.62 tff(56,plain,
% 0.45/0.62 (![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.45/0.62 tff(57,plain,
% 0.45/0.62 (![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[56, 46])).
% 0.45/0.62 tff(58,plain,
% 0.45/0.62 ((~![U: $i, X: $i, Y: $i] : (~(((~member(U, universal_class)) | (~((U = Y) | (U = X)))) <=> member(U, unordered_pair(X, Y))))) | (~(((~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), universal_class)) | (~((tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = Y!8) | (tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = X!9)))) <=> member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), unordered_pair(X!9, Y!8))))),
% 0.45/0.62 inference(quant_inst,[status(thm)],[])).
% 0.45/0.62 tff(59,plain,
% 0.45/0.62 (~(((~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), universal_class)) | (~((tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = Y!8) | (tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = X!9)))) <=> member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), unordered_pair(X!9, Y!8)))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.45/0.62 tff(60,plain,
% 0.45/0.62 (((~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), unordered_pair(X!9, Y!8))) | member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), Z!7)) | member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), unordered_pair(X!9, Y!8))),
% 0.45/0.62 inference(tautology,[status(thm)],[])).
% 0.45/0.62 tff(61,plain,
% 0.45/0.62 (member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), unordered_pair(X!9, Y!8))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[60, 37])).
% 0.45/0.62 tff(62,plain,
% 0.45/0.62 ((((~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), universal_class)) | (~((tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = Y!8) | (tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = X!9)))) <=> member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), unordered_pair(X!9, Y!8))) | (~((~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), universal_class)) | (~((tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = Y!8) | (tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = X!9))))) | (~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), unordered_pair(X!9, Y!8)))),
% 0.45/0.62 inference(tautology,[status(thm)],[])).
% 0.45/0.62 tff(63,plain,
% 0.45/0.62 ((((~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), universal_class)) | (~((tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = Y!8) | (tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = X!9)))) <=> member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), unordered_pair(X!9, Y!8))) | (~((~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), universal_class)) | (~((tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = Y!8) | (tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = X!9)))))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.45/0.62 tff(64,plain,
% 0.45/0.62 (~((~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), universal_class)) | (~((tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = Y!8) | (tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = X!9))))),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[63, 59])).
% 0.45/0.62 tff(65,plain,
% 0.45/0.62 (((~member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), universal_class)) | (~((tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = Y!8) | (tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = X!9)))) | ((tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = Y!8) | (tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = X!9))),
% 0.45/0.62 inference(tautology,[status(thm)],[])).
% 0.45/0.62 tff(66,plain,
% 0.45/0.62 ((tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = Y!8) | (tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = X!9)),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.45/0.62 tff(67,plain,
% 0.45/0.62 ((~((tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = Y!8) | (tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = X!9))) | (tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = Y!8) | (tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = X!9)),
% 0.45/0.62 inference(tautology,[status(thm)],[])).
% 0.45/0.62 tff(68,plain,
% 0.45/0.62 ((tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = Y!8) | (tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = X!9)),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.45/0.62 tff(69,plain,
% 0.45/0.62 (tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)) = X!9),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[68, 44])).
% 0.45/0.62 tff(70,plain,
% 0.45/0.62 (member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), Z!7) <=> member(X!9, Z!7)),
% 0.45/0.62 inference(monotonicity,[status(thm)],[69])).
% 0.45/0.62 tff(71,plain,
% 0.45/0.62 (member(X!9, Z!7) <=> member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), Z!7)),
% 0.45/0.62 inference(symmetry,[status(thm)],[70])).
% 0.45/0.62 tff(72,plain,
% 0.45/0.62 (member(X!9, Z!7)),
% 0.45/0.62 inference(and_elim,[status(thm)],[41])).
% 0.45/0.62 tff(73,plain,
% 0.45/0.62 (member(tptp_fun_U_0(Z!7, unordered_pair(X!9, Y!8)), Z!7)),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.45/0.62 tff(74,plain,
% 0.45/0.62 ($false),
% 0.45/0.62 inference(unit_resolution,[status(thm)],[39, 73])).
% 0.45/0.62 % SZS output end Proof
% 0.45/0.62 % E exiting
%------------------------------------------------------------------------------